# Mathematics Colloquium

## Using Computer Animations to Help Teach Mathematics

### When

September 28, 2018 | 2:30 - 3:30 p.m.

### Where

Campbell Hall 443

### Speaker

Mr. Michael Pogwizd

### Abstract

In this presentation, I share a collection of online images, animations, and videos designed to help students better understand mathematical concepts, ranging from high-school algebra to real analysis. Depending on their level of difficulty, chalk-board explanations of these concepts can require 10-20 minutes.

The visuals introduced in this presentation will do three things: 1), they will greatly reduce the amount of time needed to explain concepts; 2) they will increase the students’ understanding of the concepts; and 3) they will make learning math entertaining – not just an end unto itself, but a great way to improve retention.

My goal is to demonstrate to members of the Math Department the advantages of using these visuals in teaching and tutoring. All animations are available to use for free and can be found on my UAB website.

## Spectral Theory for Systems of Ordinary Differential Equations with Distributional Coefficients

### When

September 14, 2018 | 2:30 - 3:30 p.m.

### Where

Campbell Hall 443

### Speaker

Rudi Weikard, Chair and Professor, Department of Mathematics, University of Alabama at Birmingham

### Abstract

We discuss the spectral theory of the first-order system $Ju'+qu=wf$ of differential equations on the real interval $(a,b)$ when $J$ is a constant, invertible skew-Hermitian matrix and $q$ and $w$ are matrices whose entries are distributions of order zero with $q$ Hermitian and $w$ non-negative. We do not require the definiteness condition customarily made on the coefficients of the equation.

Specifically, we construct associated minimal and maximal relations, and study self-adjoint restrictions of the maximal relation. For these we construct Green's function and prove the existence of a spectral (or generalized Fourier) transformation.

## Classical Matrix Inequalities and their Extensions

### When

May 2, 2018 | 2:30 - 3:30 p.m.

### Where

Campbell Hall 443

### Speaker

Tin-Yau Tam, Chair and Professor, Department of Mathematics and Statistics, Auburn University

### Abstract

We will discuss some classical matrix inequalities and their extensions including Schur-Horn inequalities, Sing-Thompson’s inequalities, Weyl-Horn’s inequalities, Bhatia’s inequality etc. Most of them are related to my new book *Matrix Inequalities and Their Extensions to Lie Groups*.

## Floating Mats and Sloping Beaches: Steklov Problem on Domains with Corners

### When

April 13, 2018 | 2:30 - 3:30 p.m.

### Where

Campbell Hall 443

### Speaker

Leonid Parnovski, University College London

### Abstract

I will discuss recent results on the asymptotic behaviour of eigenvalues of Steklov operators on domains with corners. These results are rather surprising: the asymptotics depends on the arithmetic properties of the corners.

## Some Sylvester-type Matrix Equations and Tensor Equations over the Quaternion Algebra

### When

April 6, 2018 | 2:30 - 3:30 p.m.

### Where

Campbell Hall 443

### Speaker

Zhuo-Heng He, Auburn University

### Abstract

Sylvester-type equations have many applications in neural network, robust control, output feedback control, the almost noninteracting control by measurement feedback problem, graph theory, and so on. In this talk, we consider some Sylvester-type matrix equations and tensor equations over the quaternion algebra. We present some necessary and sufficient conditions for the solvability to these Sylvester-type matrix equations and tensor equations over the quaternion algebra. Moreover, the general solutions to these quaternion matrix equations and tensor equations are explicitly given when they are solvable. We also provide some numerical examples to illustrate our results.

## Elementary and Advanced Perspectives of Measurement and Ratio

### When

March 30, 2018 | 2:30 - 3:30 p.m.

### Where

Campbell Hall 443

### Speaker

James Madden, Louisiana State University

### Abstract

Measurement, ratio, and proportion are topics in elementary school mathematics, yet there are profound connections to current research in algebra and analysis, e.g., the theorem of Hölder on archimedean totally-ordered groups, the Yosida Representation Theorem for archimedean vector lattices, and my own work interpreting the Yosida Theorem in point-free topology. In this talk, I will trace the history of ratio from Eudoxus to "point-free Yosida", with stops along the way to examine interactions between academic mathematics and the mathematics taught in school.